Advertisements
Advertisements
प्रश्न
Read the following statement :
An equilateral triangle is a polygon made up of three line segments out of which two line segments are equal to the third one and all its angles are 60° each.
Define the terms used in this definition which you feel necessary. Are there any undefined terms in this? Can you justify that all sides and all angles are equal in a equilateral triangle.
Advertisements
उत्तर
The terms need to be defined are
- Polygon: A closed figure bounded by three or more line segments.
- Line segment: Part of a line with two endpoints.
- Line: Undefined term.
- Point: Undefined term.
- Angle: A figure formed by two rays with one common initial point.
- Acute angle: Angle whose measure is between 0° to 90°.
Here undefined terms are line and point.
All the angles of equilateral triangle are 60° each ...(Given).
Two line segments are equal to the third-one ...(Given).
Therefore, all three sides of an equilateral triangle are equal, because, according to Euclid’s axiom, things which are equal to the same thing are equal to one another.
APPEARS IN
संबंधित प्रश्न
Give a definition of the following term. Are there other terms that need to be defined first? What are they, and how might you define them?
line segment
In the following figure, if AC = BD, then prove that AB = CD.
In how many points two distinct lines can intersect?
It is known that if x + y = 10 then x + y + z = 10 + z. The Euclid’s axiom that illustrates this statement is ______.
In Ancient India, Altars with combination of shapes like rectangles, triangles and trapeziums were used for ______.
“For every line l and for every point P not lying on a given line l, there exists a unique line m passing through P and parallel to l ” is known as Playfair’s axiom.
Attempts to prove Euclid’s fifth postulate using the other postulates and axioms led to the discovery of several other geometries.
Solve the following question using appropriate Euclid’s axiom:
In the following figure, we have AB = BC, BX = BY. Show that AX = CY.
The following statement is true or false? Give reason for your answer.
There are an infinite number of lines which pass through two distinct points.
The following statement is true or false? Give reason for your answer.
A terminated line can be produced indefinitely on both the sides.
